Wave dispersion in viscoelastic FG nanobeams via a novel spatial–temporal nonlocal strain gradient framework

Ebrahimi, Farzad; Khosravi, Kimia; Dabbagh, Ali

doi:10.1080/17455030.2021.1970282

Cited by 6 publications

(4 citation statements)

References 93 publications

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“…, a 7 = a 5 1 + aa 4 . The system of equations ( 39) and (40) gives the following characteristic equation…”

Section: Problem Formulationmentioning

confidence: 99%

“…Dabbagh and Ebrahimi’s 39 enhancement of the structural elements’ stiffness and reducing their weight can be made possible by arranging nanocomposites in an auxetic form. Ebrahimi et al 40 stated that there is a correlation between nonlocal time and space in the nanostructures which are attacked by waves whose length lies in the range of the nanostructure’s intrinsic characteristic lengths. Ebrahimi and Dabbagh 41 studied the wave dispersion analysis of heterogeneous functionally graded (FG) nanosized beams in the framework of a nonlocal strain gradient higher-order beam theory.…”

Section: Introductionmentioning

confidence: 99%

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The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

Youssef

Al-Lehaibi

2022

The Journal of Strain Analysis for Engineering Design

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In this work, the two-temperature dual-phase-lag theorem has been used to present an analytical mathematical model for calculating the vibration in a viscothermoelastic nano-resonator. The governing equations have been derived when a simply supported nano-resonator is exposed to a ramp-type thermal load and static pre-stress. The governing equations have been solved by using a direct method and obtained the solution in the Laplace transform domain where the inversions of the Laplace transform have been calculated by using the Tzou approximation method. The increments of the dynamic and conductive temperatures, volumetric deformation, and stress regarding the resonator length for various cases of temperature type, static-pre-stress, and viscothermoelastic properties with different values of ramping heat parameter have been presented in figures and studied. The parameter of the two-temperature model, static pre-stress, ramp-type heat parameter, and viscothermoelastic parameter has a significant impact on all functions studied. The ramping time parameter may be utilized to change the thermal and mechanical properties of the nano-resonator.

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“…, a 7 = a 5 1 + aa 4 . The system of equations ( 39) and (40) gives the following characteristic equation…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

Youssef

Al-Lehaibi

2022

The Journal of Strain Analysis for Engineering Design

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show abstract

“…[12][13][14][15] Recently, it has been shown that the dynamic characteristics of nanostructures depend not only on nonlocal and length scale terms. In the methods proposed in Ebrahimi et al, [16][17][18] an interrelation between spatial and temporal nonlocality has been recommended.…”

Section: Introductionmentioning

confidence: 99%

Free vibrations of Timoshenko nanoscale beams based on a hybrid integral strain- and stress-driven nonlocal model

Oskouie

Ansari

Rouhi

2023

The Journal of Strain Analysis for Engineering Design

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Several non-classical elasticity theories are used for considering the size-dependent behavior of structures at small scales. The nonlocal theory is widely used to reflect the softening behavior of material at small scales, and theories like the strain gradient theory are employed to reflect the hardening behavior. In this article, the most general form of integral strain- and stress-driven nonlocal models with two nonlocal parameters is developed which is able to consider both hardening and softening influences simultaneously. To this end, it is considered that the stress field at the entire points of the domain is a function of strain field of the entire points of the domain. The free vibration problem of first-order shear deformable beams is solved herein. The integral form of governing equations and associated boundary conditions are obtained first, and then directly solved in a numerical approach. Through developing an efficient matrix formulation and using differential and integral matrix operators, the discretized governing equations are obtained. The simultaneous effects of strain- and stress-driven nonlocal parameters on the natural frequencies of fully clamped, fully simply-supported, and clamped-free nanobeams are investigated. The results indicate that the paradox related to the behavior of clamped-free nanobeams is resolved using the presented integral nonlocal formulation. Also, it is revealed that it is possible to find some specific values of nonlocal parameters at which the prediction of hybrid nonlocal model coincides with that of classical elasticity theory.

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“…Accordingly, various researchers conducted mathematical modeling of nanostructures containing fluid based on the NSGT. It should be mentioned that higher-order shear deformation theories (HSDTs) provide exacter responses to this topic (Dabbagh et al, 2021; Ebrahimi et al, 2019a, 2021c, 2021d, 2022). Within this context, Mahinzare et al (2017) inspected the small-scale impacts on the stability of the single-walled CNTs conveying viscous fluid based on the nonlocal strain gradient shell theory.…”

Section: Introductionmentioning

confidence: 99%

Hygro-magneto-thermally induced vibration of spinning viscoelastic Y-shaped bifurcated tubes containing magnetic fluid based on nonlocal strain gradient theory

Sivaraman

Kumar

Patra

et al. 2022

Journal of Intelligent Material Systems and Structures

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The vibration and stability of spinning viscoelastic Y-shaped bifurcated nanotubes conveying fluid in complex environments by considering additional concentrated masses and springs are studied based on the nonlocal strain gradient theory (NSGT). A detailed investigation is also performed to clarify the effect of influential parameters such as Knudsen number, magnetic nanoflow, scale parameter ratio, spin speed, fluid velocity, downstream bifurcation angle, viscoelastic coefficient, attached springs, localized masses, boundary conditions, and magneto-hygro-thermal environments on the system dynamics. The size-dependent dynamical equations of the system are derived utilizing Hamilton’s principle. The Galerkin discretization scheme is adopted, and the eigenvalue problem is numerically solved. Campbell diagrams, forward and backward frequencies, divergence and flutter instability maps are acquired. Besides, the static instability threshold of the system is determined analytically. Results revealed that although the magnetic nanoflow has a decreasing effect on system vibrational frequencies, it delays the occurrence of the dynamical instability and prevents the buckling phenomenon. It is demonstrated that by considering simultaneous stiffness-softening effects induced by nonlocality and hygro-thermal environments, the flutter instability could occur instead of divergence condition in the system stability evolution. The present modeling and results could be applied as a benchmark for the performance improvement of innovative bi-gyroscopic nanofluidic devices.

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Wave dispersion in viscoelastic FG nanobeams via a novel spatial–temporal nonlocal strain gradient framework

Cited by 6 publications

References 93 publications

The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

Free vibrations of Timoshenko nanoscale beams based on a hybrid integral strain- and stress-driven nonlocal model

Hygro-magneto-thermally induced vibration of spinning viscoelastic Y-shaped bifurcated tubes containing magnetic fluid based on nonlocal strain gradient theory

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